To travel between cities, Mexico has an excellent bus network with comfortable, frequent, and reasonably priced bus services. Most towns have one bus terminal for long-distance buses (big cities may have several). Bus services exist in various classes. There are deluxe buses and first-class buses. Both classes offer comfortable services, with designated seats, air-conditioning, adequate legroom, a toilet, and movies. Second class buses serve smaller towns and shorter routes and provide cheaper but slower service on intercity routes. They stop anywhere to pick up passengers, and there are no designated seats (you might have to stand). For second class buses, you can usually buy your ticket on the bus, with first or deluxe class buses you buy your ticket in the bus terminal.
There is only one passenger train in Mexico, "El Chepe," which travels from Chihuahua to Los Mochis, passing through the Copper Canyon. Another option to travel from city to city could be to fly. Mexico has several domestic airlines, some of them offering tickets for very low prices, which can take you to the more distant destinations. Keep in mind that Mexico is a huge country, for some destinations taking a bus will take ages and taking a flight can even be cheaper for this kind of trips.